Amplifier circuits



Jun 2, 19,42. Y J, M, WEST I 2,284,855

AMPLIFIER `,CIRCUITS I I mieu Aug'. 1e, A193s;

BV J."

ATTQNEV Patented June2; 1942 t .A s r UNrrEos'rA'n-:s y PATENT i OFFICEf ammira cmcurrs Julian` West; RidgewoodrN. J.. assigner` to BeilTelephone Laboratories, Incorporated, New York, N. Y., a corporation ofNew York l Application August 16, 1939, Serial No. 290,354 l 8 Claims.(Cl. 179-111) I This invention relates to amplifier circuits shift as tobring about phase coinciderwe the and more particularly to negativefeedbackamfeedback voltage is equal to or greater than the plifiers sodesigned as tovbeeifective over a wide effective input voltage theamplier is unstable band of frequencies. VIt f object is to provide butif the feedback voltage is less than the input for al high and`uniforminternal lopor ,le voltagathere is no instability. An`exceptional gain over the `whole bando! frequencies to be u case isillustrated in Nyquist Patent 1,915,440 of transmitted whilestillmaintaining a` substan- June `2'1, M1933. 4However, the type ofstability tial margin of safety against singing` More spe thereindisclosed is not absolute and such syscically the invention relates toso modifying tems tend to become unstable when the amplithe cut-offcharacteristic on the lower side of l0 iler gain islreduced. lo

a band to be transmitted with a negative feed- To insurel completestability of the `amplifier back amplifier that the gain around thefeedagainst singing it is, therefore, necessaryito so` back loop has ahigh value over a band to be proportion the different parts of thecircuit that transmitted and u falls to less than unity before beforethe condition of phase coincidence is a phase shift is introduced whichwould pro-l5 reached, the feedback voltage shallhave been duce singing.l attenuated to a value less than the effective The benefits to bederived from the use of feedinput voltage. This requirement may `beexback are described in an article by H. S. Black. i pressed in terms ofcertain 4transmission on Stabilized feedback amplifiers," Bell System Aparameters of the circuit as follows: If the volt- Technicai Journal,January 1934. y Principal age gain or transfer ratio from the input tothe among these benefits are the stabilization of the output of theamplifier be denoted by a and v effective amplification inthe presenceof variathemvoltage transfer ratio ofthe feedback path tions of theenergizing potentialsl applied tothe inthe reverse `direction by thenthe vector amplifier vacuum tube and the diminution of the ratio of thefeedback voltage to the resultant effects of non-linear distortion.Thesebeneiitaz input voltage on the amplier is equal to the l areobtained when the magnitude and phase of product m3 where a may have alarge value the voltage feedback to the amplifier input are over a wideportion of the frequency spectrum. such as to produce a diminution oftheeffective For complete stability, however, it is necessaryamplification, and the extent to which thebenethat the magnitude of thea become less than fits' are" realized is substantially proportional tol0 unity before its phase angle becomes Zero. the amount by which theamplification is diL The vectorquantity n the real part of whichminished is hereinafter called the loop gain, deflnesthe p `Thedegenerative action is provided by so denetl change in amplitude andphase experienced signingLthe amplifier andthe `feedback circuit by avoltage wavein traversing .the ampliner that, when .thefrequency 'hassome convenient` 85 and the feedback path in sequence. This change valuenear the middle ef the desired operating is made up essentially of `twoparts, rst a conrange, the effective input voltage is in exact stant`amplification and aconstant phase shift phase opposition to the feedbackvoltage. The representing the effect of the amplification faceffectiveinput voltage is reduced in comparison tors of the vacuurntubes and,second. a variable with the voltage from thelnput wave source and 40ldiminution of the amplitude and a variable the amplification of thesystem is diminished in phase shift representingthe transmission loss inproportion; As the'y frequency departs from this the passive networks ofthe system. Since the `near mid-point value the phase of the feedbackpart contributed by the vacuum tubes is convoltage changes progressivelyuntil at some frestant, all of the `variation of a is represented byquency, usually outside the operating range, it the variation. of thetransmission loss of the pascomes into phase coincidence with theeffective sive networks. -These passive networks include, input voltage.At this point the amplifier mayA of course, notonly the circuit from theoutput become unstable andI develop oscillations. This of the last stageto the input of a previous stage is most likely 'to occur at frequenciesabove the but include also the passivecoupling and other operating rangebut if suitable precautions have networks associated with and betweenthe tubes been taken to-avoid this then it" may occur at `of theamplier. ysome 'frequency below the operating range. By using pureresistances for thefeedbaclr Whether the circuit develops oscillationsor not v and coupling networks it would be possible theodepends `uponthe relative values or the reed- "retically to make up constant in bothampliback and the input voltage.` If with such phase tude and phase atall frequencies and thereby off range and by the rate provide for anydesired amount of feedback and an unlimited operating frequency range.In practice, however, this is impossible because of the presence ofunavoidable parasitic reactances in the system. At high frequenciesthese parasitic reactances consist primarily of shunt capacitance, suchas those Within the tube, or of series inductances; and at lowfrequencies they consist primarily of` series capacitance and shuntinductances. At very high .and very low frequencies these parasiticreactances `become the sole factors determining the magnitude and thevariation of the feedback and are generally productive of phase changessuciently great to cause instability. To avoid this it is necessary thatthe magnitude of the feedback should be reduced to less than unitybefore the limiting frequency ranges are reached and suitable frequencyintervals must be allowed for this reduction.

It is desirable that the cut-o ranges in which the magnitude of thefeedback is systematically reduced should be as small as. possible inorder that the greatest operating frequency range may I be conserved. Itcan be shown that the phase shift component of a is greatly influencedby the course that its magnitude follows in the cutat which themagnitude diminishes. In the amplifier of this invention the Ydiminutionof a is made to follow certain preferred courses which represent optimumcharacteristics in the sense that they permit Vthe use of maximumamounts Voi? feedback and vinvolve the minimum loss of useful frequencyrange while at the same time insuring complete stability againstsinging.

The invention will be better understood by reference to the followingspecification and the accompanying drawing in which:

Fig. 1 is a simplified diagram of a circuit incorporating my invention;

Fig. 2 is a detail of part of the network of Fig. 1;

Figs. 3 and '4 show curves which will explain the manner in which theinventionv is carried out; and

Fig. 5 shows a modified circuit my invention.

'I'he general theory underlying the behavior of such circuits as areshown in Fig. 1 is set forth in some detail Ain the patent to Bode2,123,178 of July 12, 1938, and need not be included here. The inventiontherein disclosed is of a broad nature and in one of its specic formsillustrates the design of a feedback circuit which will appreciablyimprove the 'cut-off characteristic on i the upper side of thetransmitted band while still maintaining a safe margin against singing.In this invention the purpose is, specifically, to im; prove the cut-offcharacteristics on the lower side of the transmitted band withoutdeleteriously affecting the upper limit and while still maintaining themargin of safety against singing.

One of the advantages which I find accruing from the redesign of the anetwork in accordance with my invention is a large reduction in the sizeof some of the elements associated with this circuit This isparticularly true of the so-called blocking condensers between adjacenttubes, these in some instances being reduced by a factor of as much as100. This reduction not only contributes to economy of cest and economyof space, but also contributes to a reduction of the parasiticcapacities effective for the high fre- A including the outputtransformer T2.

quencies which are inherent to a greater or less extent in suchcircuits.

As pointed out in the patent to Bode and elsewhere above it is essentialthat the phase shift through the a circuit shall not-exceed 360 degrecs.Since for an odd number of amplifier stages, such as in Fig. 1, therewill be a net phase change of 180 degrees due to the amplifier tubesthemselves, it is evident ,that the phase shift over the passivenetworks of the a loop inust not be allowed to exceed 180 degrees aslong as a is greater than unity. The extent to which it falls below thisat any frequency is a measure yof the margin againstI singing at thatfrequency. A full understanding /f'of the behavior of a given circuitrequires then, among other things, a knowledge of the a gain around thelo'op and a knowledge of the phase shift both as functions of frequency.

In the circuit of Fig. 1, there are shown three stages of amplification,with the usual batteries omitted for simplicity, and associated with thethree tubes are cathode networks Z141, Zxz, Zka. primarily forestablishing a self-bias. There are also the load circuits Zrl, Zig, ZB,the latter also There are condenser-resistance coupling between stages Iand 2, between 2 and 3 and between 3 and I, the

incorporating f last constituting essentially the or feedback circuit.'I'he load circuits are shown asresistive with a resistance-condenserfilter, all well known in the art, but it is to be understood that thesemay take on the form 'of any suitable impedance.

At any one frequency one may find the insertion loss due to each ofthese networks and find the phase shift due to each network. The totalloss, preferably expressed on a decibel scale. and the total phase shiftdue to the passive part of the a circuit will be the sum of these. Ifthis shift is near to but below degrees, then one may set the total gaindue to the tubes equal to the total loss of the coupling and othernetworks at that frequency so that the net gain around the loop at this`frequency is equal to unity. If for any frequency the shift issubstantially below 180 degrees then the gain may be correspondinglyraised and the amount of feedback correspondingly increased, that is,the insertion loss due to the passive networks may be reduced. However,such a change usually brings in an additional change in phase so thatthe permissible increase in gain is limited. It is essential that at nopart of the frequency spectrum where the phase shift due to thesenetworks exceeds 180 degrees shall the magnitude of a exceed unity.

While the three coupling circuits are shown as much the same ascondenser-resistance combinations they will, in general, be of differentimpedance. In this figure, moreover, it will be noted that one of thecouplings, namely, that between stages I and 2, has the resistiveportion made up of two series resistances R1 and Rz, the latter of whichis shunted by a condenser C2, these being proportioned as will bedescribed below, the combination and proportioning in this couplingbeing illustrative of and constituting an important part of myinvention.

For a better understanding of the ideas underlying this inventionreference may be made to Fig. 2 showing a four-terminal networkcorresponding to the coupling circuit just mentioned. If e1 is theimpressed and e2 the output voltage or attenuation or the sent Rn bykKRi.

` -Timpedanc'e of cois `will beteken; for illustrative purposes, i

y virtuallyshorted by cz so that proaches curve B;

increase the Amere increase assaut network and this will be a functionof frequency. Thisattenuatlon may conveniently be expressed in .decibelsby using the logarithm of the `real part of e/ei in the relation.

in the higher frequencies, `but a substantial decreaseat the lowerfrequencies. In fact, it can be shown that the area si for the regionvof increase of phase lshift taken to infinite frequency is equal tothearea s: for the region of decrease of phase shift taken to zerofrequency.

also in the analysis of the network it will be convenient `to express Riin terms of an arbitrary unit such that R1 is taken as unity and torepre- It will also'be convenient to express he. impedance of" the`condenser c1 in terms of a referencecapacitance' `co whose impedance atareference frequency fo-is" I n "JmT-T TJRI (2) Then at any otherfrequencyttaking Ril, the

The capacitanceof cz representedby a c KCI For K=0` (resistance=`R1 andcae- 0l theattenuation is `given by curve A of Fig. 3. FOLK- #4,

but still keeping cz=0, the attenuationisdecreased, the curvebeingshifted toward :lower frequencies as` shown by `curve"B. If, on theother hand, the grid leakis" made upof Brand KRi, the latter shunted bycapacitance cz, then theattenuation curve` may `with proper proper--tioning take the forrmof curveC. "l'hisl is evibd It is this phenomenonthat I use in my invention.v The delay in building up of phase shift asone goes'` to lower frequencies permits a substantial increase in" theattenuation` before the critical phase shift of 180 degrees is reached.

This in turn permits allarger amount of gain by by means of thetubesandthusalarger value of ,iover the transmission band, there stillbeing a fall in `value Df'ap toless than unity; before a phase shift ofldegrees is brought about; `x Y i By direct transfer from the set ofphase shift to the set of attenuation curves of Figii (for whichs2-Kila) one an readily, for any assumed :value of "phase` shift f asingle coupling network of this` type, plot acurve showing thefamount oflossdue to the network for different values of K .Such-.a curve is shownat D for m50 degrees and it'wiil. be observed that there is amaximumloss of about 17 decibels atx-:2.5 and thatthis ocours,=

at about 4Il now for a total 'maximum phase shift shift maybe pennittedin one of the coupling dent, for at highfrequencies the portion KRi is lthe effective grid impedance is R1 and the attenuation is; relativelyhigh. `As the frequency lowers, the impedance of ci increases, whichwould increase the attenuation but vthe impedance of. c: also increases,

thus retarding the increase of attenuation. llt"t 5 still lowerfrequencies the impedance` of ci be`- comes controlling and theattenuation curve apjf shown and inevery case it will be noted that theeffect of ce is to decrease the slope of the' atten-` uation curve forthe intermediate frequencies below that for whichcz is virtually a shortcircuit KRi. Other similar families of curves could be plotted for ethervalues of ci.

y r frequencies but at low becomes practically ineffective. At

*to only 4 decibels.

networks, then it, is seen from curve Dvthat the maximum insertion lossfor such a coupling net- 'shows that the loss for =50`degrees, amountsSimilar curves could be plotted for other values of o `and some of theresults are tabulated below. .From this one obtains additionalinformation for the design of the "amplifier circuits: i

Maximum Maximum K lossin lossior decibels lil-0 las n 4 60 1+ .21 e k 124 9 supplementing the theory presented inthe yBode patent referred 'toabove, vit Vmay be here pointed out. `without derivation, that theexpres- These changes in the'form of the attenuation curves areaccompanied by `changes in the phase shift curves as shown in the upperportion of" Fig.` 3. Curves A', B and C' From curve B'lit is seen Ycorrespond to curves A. B andlC.

that themere increase of K (or, `equivalentlyy the.

of ci) -delays somewhat the build ing up of phase 'shift 'as onegoes-'to` lowerifrequencies, but the form of .the curve is not altered.The addition of capacitancev c: correspondins to curves B and B bringsabout,

however,a substantial change in fom-characterized by a substantialinorease in phase shift ro to me circuit sionfor the a gain foi' thecircuit of Fig. 1 inthe low frequency range where the high frequencyparasitic capacities may be neglected is given by [1 +s..,zx, Saz"z.,+zv,+zi,]

` 1 cf` Z', 14+Sazzx, u I Ziff-Zefijzrs i of the combined passingnetworks ofless than degrecs it is agreed that 50 degrees of the phase twork will be `obtained for a value of X=2.5. A v comparison with thecorresponding case czv--O finite and that the source of B supply is ofzero impedance.

A convenient design procedure is to break this expression for ri intofour factors as follows:

To a very close approximation this is the only significant term at themiddle of the useful band of the amplifier. It, therefore, gives thenominal a gain. 'I'he use of condenser-resistance filters in the Bsupply leads causes this gain to rise a Y few decibels at very lowfrequencies. The effect of this factor on the p'gain of the circuit isshown by curve I of Fig. 4 plotted with reference to anominal gain of 40decibels and against the logarithm of frequency.

This term represents the effect of the local feedback produced by theresistances used for selfbiasing the tubes. In general, this termcontributes a major part of the low frequency cutoff. For example, withone type of tube known as Western Electric 7650P tube and the value ofresistance to give the correct bias voltage, the gain is reduced 21decibels at low frequencies by this factor. The effect of this factor onthe a gain is shown by curve 2 of Fig. 4.

3 d I: l Z2 (6) r Z.,+Z..,+z., Z.,+Z,+Zp This term represents'the Veectof any two of Athe simple blocking condenser grid leak combinations.'Ihe blocking condensers yare preferably made so small that this factorbegins to reduce the a gain at the point where the 2nd factor becomesless effective. The effect of this factor on the a gain is shown bycurve 3 of Fig. 4, reaching a slope of 12 decibelsper octave.

This term represents the effect of the remainin grid blocking condensergrid leak combination with shunt capacitance, the results being shown bycurve 4 of Fig. 4 and corresponding closely in form to the attenuationcurves of Fig. 3. It is this configuration that I find effective in thelow In view of the delay in the building'up of the l phase shift whichaccompanies the introduction of the capacitance c2 it becomes evidentthat the condenser c1 may be substantially reduced without introducingan excessive additional phase shift. This is a marked advantage in thatthe A,use of a smaller condenser is cheaper and more economical ofspace, but still further because the reduction in the physicaldimensions of the conper side of the frequency band to be transmitted.In practice I nnd that this capacity may be decreased by. a factor of asmuch as 10 or 100.

While the description thus far has been on the basis of altering thecoupling network between stages I and 2 of Fig. 1, it should be pointedout that the total alteration desired may be accomplished at one step asdescribed or may be distributed in any desired portions among theplurality of coupling circuits. Certain advantages would accrue fromsuch distribution, for each of the blocking condensers could then bereduced with a corresponding reduction in parasitic capacities for highfrequencies. On the other hand, it will be noted that such distributionwill call for a larger number of elements, represented by the pluralityof capacitances c2. Depending upon the circumstances, therefore, it maybe advantageous in the one case to distribute the adjusting factors andin some other cases to conne it to one of the coupling networks. Also,while in the description the coupling network has been shown betweenstages l and 2 of Fig. 1, there would be certain advantages at times inplacing it in one of the other positions. In some cases, for example, Iwould prefer to place it in the circuit representing the couplingbetween stages 3 and l (see Fig. 5). Such a location has a certainadvantage for in general the impedance Z; in the output circuit would besmall compared to Zrl and Zie. In that case the resist-ance R1 of Fig. 2may be made appreciably smaller without this portion of the circuitacting as an appreciable shunt to Z.

Thus far in the description reference has been largely to pure ohmicresistances. Itis to be understood, however, that the impedances R1 andKRi of Fig. ,2, as well as the resistances of the other couplingcircuits and of the loads, may be reactive. As a matter of fact, I nd itadvantageous at times to include with R1 a suitable amount of inductivereactance as shown in Fig. 5. The principles described above holdequally well and the application of the invention to any one iparticular case would then involve the plotting of attenuation and phaseshifting curves which involve more, but only slightly more, labor.

What is claimed is:

1. A wave amplifying system comprising a plurality of vacuum ltubeamplifying devices, impedance networks coupling said devices intandem,.a feedback path coupling the output circuit of the last of saidtandem connecteddevices with the input circuit of the first of saiddevices and an impedance network included in said feedback path, saidimpedance networks each comprising a plate circuit branch and a gridcircuit branch,

said networks having a combined attenuation which is substantiallyconstant and small relative to the combined gain of said amplifyingdevices at frequencies in an assigned operating range, which increaseswith the decrease'of frequency just below said operating range, andwhich has a progressively changing phase as the frequency is stillfurther lowered, means for delaying the building up of phase shift withdecreasing fre- .quencies said means comprising capacitance denser c1reduces its capacity to ground, which f latter contributes totheparasitic capacitiesat high frequencies. favorably on the 'cut-olfcharacteristic at the up- Thus the combination reacts shunting a portionof the grid circuit branch of l one of said coupling impedances, themagnitude of the.'y capacitance being such as to delay the building upof phase shift with decreasing frequencies until a frequency-level isreached at which the net gain around the feedback loop is less thanunity.

2. A wave amplifying system comprising a pludem. a feedback path -of thetwo condensers being necting said grid leak impedance said amplifierloop circuit,

. 2528455 rality of vacuum, tube amplifying devices, im-

pedance networksv coupling said devices in tancoupling the outputcircuit of the last of said tandem connected devices with the inputcircuit of the first of said devices l and an impedance network includedin said feedback path, said impedance` networks having a combinedattentuation which is substantially constant and small relative tothecombined gain of said amplifying devices at frequencies in an said givenfrequency decibels per octave of frequency until the loop gain attainsnegative value not greatly different from zero, and said portioned todiminish the loop gain at a rate between zero and 6 decibels per octaveat still lower frequencies for a short frequency interval whereby thetotal loop phase shift is held substantially different from zero at thefrequency of zero assigned operating range and -which increases as l,

the frequency decreases below said `operating range, the rate ofincrease of attenuation being at first increasingly high near theoperating range,v then low at lower frequencies, and then high at stilllower frequencies. j i

i 3. A negative feedback ampliner comprising a plurality ofamplification stages andl a feedback path around said stages for feedingback waves in gain reducing phase within a transmission frequency band.condenser grid between two `leak resistance coupling network across theresistthe transmission said amplifier including a stopping Y stages, thestopping condenser being i of such magnitude as to producesubstantiallyl i no reduction of its capacity such band but toreducethis ratio rapidly below the i transmission band, a condenser shunting apor-` tion of the resistance and of such magnitude as to substantiallyshort-circuit the portion of resistance for frequencies inthetransmission band butto permit substantial increase of the transferratio at lower frequencies, the combinedeffect the transfer ratio forthe rst two octaves of frequency below the transmission band but toreduce it at a much lower rate for the nextfew octaves and then to lowerfrequencies.

. 4. Arioop circuit discharge devices, one cathode, and the other havinga grid and a cath# ode, connections for feeding waves put of the device,and means for coupling the anode and cathode of said one device to thegrid and cathode of said other device, said means comprising animpedance connected between the plate and the cathode of said onedevice, a stopping condenser and a grid leak impedance connected inseries across said first impedancefmeans conbetween the grid and thecathode of said second device, and a condenser shunting `a impedance andhaving as to increase the phase said` loop against singing its capacityvalue such below an operating to `rapidly reduce reduce itrapidly forstill other deviceto the input of said one decibel loop gain, at leastone of said networks comprising a stopping condenser and a grid leakimpedance including in` series a resistance and a parallel combinationof a resistor and a condenser.

6. An amplifier comprising `three cascaded stages of vacuum tubesforming a closed feedback loop with each 4interstage circuit including acoupling network comprising a stopping condenser and a grid leakimpedance, in the case of each coupling network said grid leak impedancecomprising in series a resistance and a parallel combination of 'aresistance and a shunting condenser, said shunting condenser having thevalue as to increase at least several fold in comparison with conditionsin the absence of the shunting condenser the decibel value reached bythe insertion loss of the coupling networkbefore its phase shift exceeds60 degrees with` diminishing frequency below the operating frequencyrange of the amplifier. Y.

7. In a negative feedback amplifier including a plurality of stages witha feedback path for feeding waves from the output to the input in gainreducing phase throughout an operating frequency range, and includinginterstage networks of said leak resistance, said shunting capacity,

Y said grid leak resistance, the portion of said reportion of said gridleak margin of stability of frequency range for which` transmissionaround the loop has` a terially reducing said range.

5. A wave amplifying system comprising an electric space dischargeamplifier,` a feedback path extending betweenthe output and formingtherewith a closed frequency selective impedance networks included insaid loop circuit, saidnetworks being `proportioned to provide in`combination with the gain of the amplifier a relative large loop gain atfrequencies `above a given frequency van to diminish the loop gain atfrequencies below substantial gainV without mathe gain around the loopand input of i the series coupling sistance that is shunted by saidcapacity, and i capacity connected to said last-mentioned impedancebranch being proportioned with respect to one another to cause saidinterstagenetwork to have increasing attenua- -tion with decreasingfrequencies near the lower edge of the operating frequency range to amuch higher value of attenuation than would be attained without saidshunting capacity, before the phase shift produced by said interstagenetwork has reached 60 degrees and to delay increase of said phase shiftabove 6,0 degrees with further decrease of frequency until theattenuation has attaineda still larger value.

8. Thecombination of claim in which said shunting capacity, said gridleak resistance, the portion of said resistance that is shunted by saidcapacityl and said series coupling capacity are proportioned withrespect to one another to cause said phase shift produced by saidvinterstage network to have approximately the constant value of 45degrees over a range of low frequencies and to cause the attenuation toincrease with decreasing frequency within said range of low frequenciesby a factor of more than 2 to 1 on a logarithmic scale.

JULIAN M. WEST.

, 5 at a rate between 6 and 12` networks being further -pro

